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Mixtures of normal distributions: Modality and failure rate

Author

Listed:
  • Block, Henry W.
  • Li, Yulin
  • Savits, Thomas H.

Abstract

The normal density is unimodal in a strong sense as are the densities of mixtures of normals whose means are not too far apart. Consequently, by a standard result in reliability, these mixture densities have an increasing failure rate. This paper investigates how the modality of mixtures of normals and the monotonicities of the failure rate of the mixture are related.

Suggested Citation

  • Block, Henry W. & Li, Yulin & Savits, Thomas H., 2005. "Mixtures of normal distributions: Modality and failure rate," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 253-264, October.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:3:p:253-264
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    References listed on IDEAS

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    1. Schilling M.F. & Watkins A.E. & Watkins W., 2002. "Is Human Height Bimodal?," The American Statistician, American Statistical Association, vol. 56, pages 223-229, August.
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    Cited by:

    1. Tian Li & Shilu Tong & Hongtao Zhang, 2014. "Transparency of Information Acquisition in a Supply Chain," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 412-424, July.
    2. Andreas Behr & Ulrich Pötter, 2009. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models," Annals of Finance, Springer, vol. 5(1), pages 49-68, January.
    3. Liu, Fuxiang & Liu, Yanyan, 2008. "The failure rate properties of a bimodal mixture of normal distributions in an unequal variance case," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2006-2009, October.

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